The power of symmetric extensions for entanglement detection

In this paper, we present new progress on the study of the symmetric extension criterion for separability. First, we show that a perturbation of order O(1/N) is sufficient and, in general, necessary to destroy the entanglement of any state admitting an N Bose symmetric extension. On the other hand, the minimum amount of local noise necessary to induce separability on states arising from N Bose symmetric extensions with Positive Partial Transpose (PPT) decreases at least as fast as O(1/N^2). From these results, we derive upper bounds on the time and space complexity of the weak membership problem of separability when attacked via algorithms that search for PPT symmetric extensions. Finally, we show how to estimate the error we incur when we approximate the set of separable states by the set of (PPT) N -extendable quantum states in order to compute the maximum average fidelity in pure state estimation problems, the maximal output purity of quantum channels, and the geometric measure of entanglement.Comment: see Video Abstract at http://www.quantiki.org/video_abstracts/0906273

Free energy density for mean field perturbation of states of a one-dimensional spin chain

Motivated by recent developments on large deviations in states of the spin chain, we reconsider the work of Petz, Raggio and Verbeure in 1989 on the variational expression of free energy density in the presence of a mean field type perturbation. We extend their results from the product state case to the Gibbs state case in the setting of translation-invariant interactions of finite range. In the special case of a locally faithful quantum Markov state, we clarify the relation between two different kinds of free energy densities (or pressure functions).Comment: 29 pages, Section 5 added, to appear in Rev. Math. Phy

Monogamy of Correlations vs. Monogamy of Entanglement

A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results as well as present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell's theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, although, and importantly, it is stressed that not all non-local correlations are monogamous.Comment: 12 pages, 2 figures. Invited submission to a special issue of Quantum Information Processing. v2: Published version. Open acces

Bonding stability of adhesive systems to eroded dentin

This in vitro study evaluated the immediate and 6 months microshear bond strength (µSBS) of different adhesive systems to sound and eroded dentin. Sixty bovine incisors were embedded in acrylic resin and ground to obtain flat buccal dentin surfaces. Specimens were randomly allocated into two groups: sound dentin (immersion in artificial saliva) and eroded dentin (erosive challenge following a pH cycling model comprising 4 ×/day Sprite Light® drink for 10 days). Then, specimens were reassigned according to the adhesive system: etch-and-rinse adhesive (Adper Single Bond), two-step self-etch system (Clearfil SE Bond), or one-step self-etch adhesive (Adper Easy One). Polyethylene tubes with an internal diameter of 0.76 mm were placed over pre-treated dentin and filled with resin composite (Z250). Half of the specimens were evaluated by the µSBS test after 24 h, and the other half 6 months later, after water storage at 37°C. Failure mode was evaluated using a stereomicroscope (400×). Data were analyzed by three-way repeated measures analysis of variance and Tukey’s post hoc tests (α = 0.05). After 6 months of water aging, marked reductions in µSBS values were observed, irrespective of the substrate. The µSBS values for eroded dentin were lower than those obtained for sound dentin. No difference in bonding effectiveness was observed among adhesive systems. For all groups, adhesive/mixed failure was observed. In conclusion, eroded dentin compromises the bonding quality of adhesive systems over time

Monogamy of entanglement and other correlations

It has been observed by numerous authors that a quantum system being entangled with another one limits its possible entanglement with a third system: this has been dubbed the "monogamous nature of entanglement". In this paper we present a simple identity which captures the trade-off between entanglement and classical correlation, which can be used to derive rigorous monogamy relations. We also prove various other trade-offs of a monogamy nature for other entanglement measures and secret and total correlation measures.Comment: 7 pages, revtex

Effect of method of caries induction on aged resin-dentin bond of primary teeth

Background: To investigate the influence of chemical and microbiological methods of caries induction on bond degradation of adhesive systems to primary dentin.Methods: Flat dentin surfaces from 36 primary molars were assigned to three groups (n = 12) according to method to induce caries-affected dentin: (1) control (sound dentin); (2) pH-cycling; and (3) microbiological caries induction model. Teeth were submitted to caries induction for 14 days for both methods, and the sound dentin was stored in distilled water during the same period. Specimens from each experimental group were then randomly reassigned to two subgroups (n = 6) according to the adhesive system tested: two-step etch-and-rinse adhesive (Adper Single Bond 2 - SB) or two-step self-etch system (Clearfil SE Bond - CSEB). Composite buildups were constructed and sectioned to obtain bonded sticks to be subjected to microtensile (mu TBS) testing immediately or after 12 months of water aging. The mu TBS means were analyzed by three-way repeated measures ANOVA and Tukey's tests (alpha = 0.05).Results: The mu TBS values obtained to artificially-created caries-affected dentin were lower compared with sound dentin, but were not affected by method of caries induction. Water storage for 12 months reduced bond strengths, except to CSEB bonded to sound dentin.Conclusion: Chemical and microbiological methods affect similarly the stability of resin-dentin bonds in primary teeth

Adversarial hypothesis testing and a quantum stein's lemma for restricted measurements

Recall the classical hypothesis testing setting with two convex sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p ∈ P or from a distribution q ∈ Q and wants to decide from which set the points were sampled. It is known that the optimal exponential rate at which errors decrease can be achieved by a simple maximum-likelihood ratio test which does not depend on p or q, but only on the sets P and Q. We consider an adaptive generalization of this model where the choice of p ∈ P and q ∈ Q can change in each sample in some way that depends arbitrarily on the previous samples. In other words, in the kth round, an adversary, having observed all the previous samples in rounds 1, ..., κ-1, chooses p[subscript κ] ∈ P and q[subscript κ] ∈ Q, with the goal of confusing the hypothesis test. We prove that even in this case, the optimal exponential error rate can be achieved by a simple maximum-likelihood test that depends only on P and Q. We then show that the adversarial model has applications in hypothesis testing for quantum states using restricted measurements. For example, it can be used to study the problem of distinguishing entangled states from the set of all separable states using only measurements that can be implemented with local operations and classical communication (LOCC). The basic idea is that in our setup, the deleterious effects of entanglement can be simulated by an adaptive classical adversary. We prove a quantum Stein's Lemma in this setting: In many circumstances, the optimal hypothesis testing rate is equal to an appropriate notion of quantum relative entropy between two states. In particular, our arguments yield an alternate proof of Li and Winter's recent strengthening of strong subadditivity for quantum relative entropy.National Science Foundation (U.S.) (Grant CCF-1111382)United States. Army Research Office (Contract W911NF-12-1-0486

Faithful Squashed Entanglement

Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed entanglement is faithful, that is, strictly positive if and only if the state is entangled. We derive the bound on squashed entanglement from a bound on quantum conditional mutual information, which is used to define squashed entanglement and corresponds to the amount by which strong subadditivity of von Neumann entropy fails to be saturated. Our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality. The proof is based on two recent results from quantum information theory: the operational interpretation of the quantum mutual information as the optimal rate for state redistribution and the interpretation of the regularised relative entropy of entanglement as an error exponent in hypothesis testing. The distance to the set of separable states is measured by the one-way LOCC norm, an operationally-motivated norm giving the optimal probability of distinguishing two bipartite quantum states, each shared by two parties, using any protocol formed by local quantum operations and one-directional classical communication between the parties. A similar result for the Frobenius or Euclidean norm follows immediately. The result has two applications in complexity theory. The first is a quasipolynomial-time algorithm solving the weak membership problem for the set of separable states in one-way LOCC or Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show that multiple provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations thereby providing a new characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published version, claims have been weakened from the LOCC norm to the one-way LOCC nor